Nowadays, the dynamics of information is one of the central topics of philosophical logic. In particular, belief revision theory (Alchourrón et al., 1985) is concerned with formalizing the notions of information state and strategies for belief change. Moreover, dynamic epistemic logic (see Van Ditmarsch et al., 2007), gives a logical account of the above concepts in the multi-agent context. On the other hand, formal learning theory sets up a computational framework for investigating the process of conjecture change (see e.g., Jain et al., 1999). Although the two paradigms of formal learning theory and belief revision/dynamic epistemic logic are interested in similar and interrelated questions, the communication between them is difficult. Learning theory is concerned with the global process of convergence in the context of computability. Belief-revision and dynamic epistemic logic focus on single steps of revision and constructive manners of obtaining new states. The goal of the course is to discuss the methodology and the benefits of the meet between `philosophy of information dynamics' and formal learning theory.
basic logic, basic computability theory, basic modal logic
This part will be a presentation of the well-established formal accounts of information dynamics: so-called AGM belief revision (based on: Alchourrón et al., 1985; Gärdenfors, 1988) and elements of dynamic epistemic and doxastic logic (partially based on: Van Ditmarsch et al., 2007).
The second introductory part will give preliminaries of formal learning theory: identification in the limit in the context of computability (based on: Gold, 1967; Angluin and Smith, 1983) and the general framework of limiting learning for arbitrary number theoretic learning functions (based on: Jain, et al., 1999).
The first link between belief revision theory and formal learning theory uses first-order structures as potential realities (instead of sets on numbers); the data that the learner uses for forming the conjectures consist of atomic formulas true in the chosen structure. This framework allows investigating AGM belief-revision policies in the iterative context of first-order inquiry. This in turn gives a way to investigate, among others, the canonicity of belief revision based learning methods (based on: Martin and Osherson, 1998).
The canonicity of certain learning functions leads to the concept of the reliability of revision methods. It has been studied in the context of possible world semantics used in modal logics of knowledge and belief. We will overview the results in this domain (based on: Kelly, 1998; Ch. 4 of Gierasimczuk, 2010; Baltag et al, 2011).
The final part of the course will overview recent results stemming from the link between formal learning theory and logical approaches to belief-revision and knowledge change. We will focus on the possibility of expressing learnability conditions in dynamic epistemic and doxastic logic (Ch. 5 of Gierasimczuk, 2010) and on the analysis of the notion of certainty from the perspective of computable learning functions (Ch. 6 of Gierasimczuk, 2010).<\li>
Nina Gierasimczuk |
Email: Nina DOT Gierasimczuk AT gmail DOT com
Homepage: http://staff.science.uva.nl/~ngierasi/
Bio:I obtained my PhD in 2010 from the Institute for Logic, Language and Computation (ILLC), University of Amsterdam, under the supervision of Johan van Benthem and Dick de Jongh. In my dissertation, titled "Knowing One's Limits. Logical Analysis of Inductive Inference" I explore the connections between formal learning theory and dynamic epistemic logic. Before that, I got my MA at the Institute of Philosophy at the Warsaw University, where I studied under the supervision of Marcin Mostowski. Currently, I am a Post-Doc researcher within the Reasoning about Quantum Interaction Project at the Institute of Artificial Intelligence and Cognitive Engineering (ALICE), University of Groningen.
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